Contemporary Mathematics 1993; 347 pp; softcover Volume: 149 ISBN10: 0821851497 ISBN13: 9780821851494 List Price: US$60 Member Price: US$48 Order Code: CONM/149
 Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twentyfive. He left behind several seminal contributions which have profoundly influenced the field and continue to provide inspiration for current research. This book is based on papers presented at the conference, "Fifty Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes, and Sums of Random Variables," held at Blaubeuren, Germany, in November 1991. Presented here for the first time is an account of Doeblin's life and work, revealing the circumstances of his tragic death in 1940. Organized into sections according to topic, the papers describe both Doeblin's original contributions as well as current developments. With contributions by top probabilists from sixteen countries, this book will interest both researchers in probability and science historians. Readership Researchers in probability and science historians. Table of Contents  Doeblin's Life and Work
 B. Bru  Doeblin's life and work from his correspondence
 K. L. Chung  Reminiscences of one of Doeblin's papers
 Coupling
 T. M. Liggett  The coupling technique in interacting particle systems
 H. Thorisson  Coupling and shiftcoupling random sequences
 Continued Fractions and Ergodicity
 M. Iosifescu  Doeblin and the metric theory of continued fractions: A functional theoretic solution to Gauss' 1812 problem
 M. Iosifescu  A basic tool in mathematical chaos theory: Doeblin and Fortet's ergodic theorem and Ionescu Tulcea and Marinescu's generalization
 M. Iosifescu and S. Kalpazidou  The nearest integer continued fraction expansion: An approach in the spirit of Doeblin
 Independent and Weakly Dependent Random Variables
 M. Csörgő, L. Horváth, Q.M. Shao, and B. Szyszkowicz  On the weighted asymptotics of partial sums and empirical processes of independent random variables
 M. Gordin  Homoclinic approach to the central limit theorem for dynamical systems
 M. Peligrad  Asymptotic results for \(\varphi\)mixing sequences
 M. Rosenblatt  The central limit theorem and Markov sequences
 Homogeneous and Nonhomogeneous Markov Chains
 I. Fleischer and A. Joffe  Behaviour of infinite products with applications to nonhomogeneous Markov chains
 E. Seneta  Applications of ergodicity coefficients to homogeneous Markov chains
 Markov Processes
 I. Cuculescu  Applications of some constructions of Markov processes
 S. P. Meyn and R. L. Tweedie  The Doeblin decomposition
 S. P. Meyn and R. L. Tweedie  Generalized resolvents and Harris recurrence of Markov processes
 Stochastic and Nonstochastic Matrices
 J. E. Cohen, Y. Derriennic, and Gh. Zbaganu  Majorization, monotonicity of relative entropy, and stochastic matrices
 H. Cohn  Products of stochastic, nonstochastic, and random matrices
 J. Hajnal  Shuffling with two matrices
 Stochastic Processes
 K. B. Athreya  Continuous time gambling problems
 E. Bolthausen  Stochastic processes with long range interactions of the paths
 A. Mukherjea  Some remarks on products of random affine maps on \((R^+)^d\)
 P. E. Nüesch  A multivariate look at E. Sparre Andersen's equivalence principle
 P. Ney and E. Nummelin  Regeneration for chains of infinite order and random maps
